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Steven F. Bartlett, 2011

Lower San Fernando Dam - 1971 San Fernando Valley Earthquake, Ca.

Main Issues in Seismic Assessment of Earthen Embankments and Dam:

Stability: Is embankment stable during and after earthquake?

Deformation: How much deformation will occur in the dam?

Two general types of analyses needed to answer these questions:

2D Dynamic Response Analysis

2D Deformation Analysis

In some approaches, these two analyses are coupled.

2-D Seismic Embankment and Slope Assessment and StabilityWednesday, August 17, 2011

12:45 PM

Lecture 9 - 2D Dynamic Analyses Page 1

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Pseudostatic Analysis

Makdisi and Seed (1978) used average accelerations computed by the

procedure of Chopra (1966) and sliding block analysis to computeearthquake-induced deformations of earth dams and embankments.

Newmark Sliding Block Analysis

Quake/W

Plaxis

FEM

FLAC

FDM

Numerically Based Analysis

This course will focus on Pseudostatic and Newmark Sliding Block Analyses using

the Makdisi-Seed (1978) Method

General Types of 2D Seismic AnalysisSunday, August 14, 2011

3:32 PM


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If the embankment and foundation materials are not susceptible to

liquefaction or strength reduction due to earthquake shaking, then the

embankment will generally he stable and no catastrophic failure is expected

(Seed, 1979).

However, if the embankment or/and foundation comprise liquefiable

materials, it may experience flow failure depending on post-earthquake factor

of safety against instability (FOSpe).

For high initial driving stress (steep geometry), the FOS will likely be much less

than unity, and flow failure may occur, as depicted by strain path A-B-C.

Example of this is the failure of the Lower San Fernando Dam.

In this lecture we will not address the effects of liquefaction on embankment

stability. This is an advanced topic taught in CVEEN 7330.

from:

Effects of LiquefactionWednesday, August 17, 2011

12:45 PM


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Pseudostaic apply a static (non-varying) force the centroid of mass to

represent the dynamic earthquake force.

Fh = ah W / g = kh W

Fv = av W/ g = kv W (often ignored)


Guidance on the Selection of Kh

Pseudostatic AnalysisSunday, August 14, 2011

3:32 PM


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Recommendations for implementation of pseudostatic analysis (Bartlett)

General comment: The pseudostatic technique is dated and should only be

used for screening purposes. More elaborate techniques are generally

warranted and are rather easy to do with modern computing software.


Representation of the complex, transient, dynamics of earthquake shaking by

a single, constant, unidirectional pseudostatic acceleration is quite crude.

Method has been shown to be unreliable for soils with significant pore

pressure buildup during cycling (i.e., not valid for liquefaction).

Some dams have failed with F.S. > 1 from the pseudostatic technique

Cannot predict deformation.

Is only a relative index of slope stability

Limitations of Pseudostatic Technique

Pseudostatic Analysis (cont.)Sunday, August 14, 2011

3:32 PM


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Layer(top tobottom)

(kN/m3)

(lb/ft3) E (kPa) v K (kPa) G (kPa) c (kPa) Ko Vs (m/s)

1 15.72 100 100000 0.37 128,205 36,496 24.37 0 0.5873 150.9

2 16.51 105 100000 0.37 128,205 36,496 24.37 0 0.5873 147.3

3 17.29 110 150000 0.35 166,667 55,556 27.49 0 0.5385 177.5

4 18.08 115 200000 0.3 166,667 76,923 34.85 0 0.4286 204.3

5 18.08 115 250000 0.3 208,333 96,154 34.85 0 0.4286 228.4

emban 21.22 135 300000 0.3 250,000 115,385 34.85 0 0.4286 230.9

Pasted from

Example Geometry

Example Soil Properties

E = Young's Modulus

= Poisson's ratio

K = Bulk modulus

G = Shear Modulus

= drained friction angle

c = cohesion

Ko = at-rest earth pressure coefficent

Vs = shear wave velocity

Pseudostatic Analysis - ExampleSunday, August 14, 2011

3:32 PM

http://c/Users/sfbartlett/Documents/GeoSlope/miscdynamic1.xlshttp://c/Users/sfbartlett/Documents/GeoSlope/miscdynamic1.xls

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Pseudostatic Results

FS = 1.252 (static with no seismic coefficient, Kh)

The analysis has been repeated by selecting only the critical circle. To do this,

only one radius point. This result can then be used with a Kh value to determine

the factor of safety, FS.


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Time [sec]

161514131211109876543210

Acceleration[g]

0.6

0.5

0.4

0.3

0.2

0.1

0

-0.1

-0.2

-0.3

-0.4

Acceleration time history

Damp. 5.0%

Period [sec]

3210

ResponseAcceleration[g]

1.4

1.35

1.3

1.25

1.2

1.15

1.1

1.05

1

0.95

0.9

0.85

0.8

0.75

0.7

0.65

0.6

0.55

0.5

0.45

0.4

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0

Response Spectrum for acceleration time history

pga = 0.6 g

Kh = 0.5 * pga

ah = 0.3 g (This is applied in the software as a horizontal acceleration).


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Reduce shear strength in stability model for all saturated soils to 80 percent of

peak strength as recommended by the Army Corp of Engineers. This is to account

for pore pressure generation during cycling of non-liquefiable soils. (See table

below.) (If liquefaction is expected, this method is not appropriate.)

Layer(top tobottom)

(kN/m3)

(lb/ft3) E (kPa) v K (kPa) G (kPa) Tan

80percentTan

Newphiangleforanalysis

1 15.72 100 100000 0.37 128,205 36,496 24.37 0.4530 0.3624 19.92

2 16.51 105 100000 0.37 128,205 36,496 24.37 0.4530 0.3624 19.92

3 17.29 110 150000 0.35 166,667 55,556 27.49 0.5203 0.4162 22.60

4 18.08 115 200000 0.3 166,667 76,923 34.85 0.6963 0.5571 29.12

5 18.08 115 250000 0.3 208,333 96,154 34.85 0.6963 0.5571 29.12

embank 21.22 135 300000 0.3 250,000 115,385 34.85 0.6963 0.5571 29.12

Pasted from

The analysis is redone with Kh = 0.3 and reduced shear strength (see below).

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36

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

101 102 103 104 105 106

107108 109 110 111 112

113114115116117118

119120 121 122 123 124

125 126 127 128129 130

131 132 133 134 135136

137 138 139 140 141142143 144 145 146 147148

149 150 151 152 153154

0.651

1

2 3

4

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34

35

36

The resulting factor of safety is 0.651 (too low). Deformation is expected for this

system and should be calculated using deformation analysis (e.g., Newmark,

Makdisi-Seed, FEM, FDM methods.)


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http://c/Users/sfbartlett/Documents/GeoSlope/miscdynamic1.xlshttp://c/Users/sfbartlett/Documents/GeoSlope/miscdynamic1.xls

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Pasted from


Newmarks method treats the mass as a rigid-plastic body; that is, the

mass does not deform internally, experiences no permanent

displacement at accelerations below the critical or yield level, and

deforms plastically along a discrete basal shear surface when the critical

acceleration is exceeded. Thus, for slope stability, Newmarks method is

best applied to translational block slides and rotational slumps. Other

limiting assumptions commonly are imposed for simplicity but are not

required by the analysis (Jibson, TRR 1411).

1. The static and dynamic shearing resistance of the soil are assumed to

be the same. (This is not strictly true due to strain rate effects

2. In some soils, the effects of dynamic pore pressure are neglected. This

assumption generally is valid for compacted or overconsolidated clays

and very dense or dry sands. This is not valid for loose sands or normallyconsolidated, or sensitive soils.

3. The critical acceleration is not strain dependent and thus remains

constant throughout the analysis.

4. The upslope resistance to sliding is taken to be infinitely large such that

upslope displacement is prohibited. (Jibson, TRR 1411)

Newmark Sliding Block AnalysisSunday, August 14, 2011

3:32 PM

http://pubs.usgs.gov/of/1998/ofr-98-113/ofr98-113.htmlhttp://pubs.usgs.gov/of/1998/ofr-98-113/ofr98-113.htmlhttp://pubs.usgs.gov/of/1998/ofr-98-113/ofr98-113.htmlhttp://pubs.usgs.gov/of/1998/ofr-98-113/ofr98-113.html

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Steps

Perform a slope stability analysis with a limit equilibrium method and find the

critical slip surface (i.e., surface with the lowest factor of safety) for the given soil

conditions with no horizontal acceleration present in the model.

1.

Determine the yield acceleration for the critical slip circle found in step 1 by

applying a horizontal force in the outward direction on the failure mass until a

factor of safety of 1 is reached for this surface. This is called the yield

acceleration.

2.

Develop a 2D ground response model and complete 2D response analysis for the

particular geometry. Use this 2D ground response analysis to calculate average

horizontal acceleration in potential slide mass.

3.

Consider horizontal displacement is possible for each time interval where the

horizontal acceleration exceeds the yield acceleration (see previous page).

4.

Integrate the velocity and displacement time history for each interval where the

horizontal acceleration exceeds the yield acceleration (see previous page).

5.

The following approach is implemented using the QUAKE/WTM and SLOPE/WTM.


Acceleration vs. time at base of slope from 2D response analysis in Quake/W.

Newmark Sliding Block Analysis (cont.)Sunday, August 14, 2011

3:32 PM


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Analysis perfromed using shear strength = 100 percent of peak value for all soils

(i.e., no shear strength loss during cycling).


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1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

101 102 103 104 105 106

107108 109 110 111 112

113114115116117118

119120 121 122 123 124

125 126 127 128129 130

131 132 133 134 135136

137 138 139 140 141142143 144 145 146 147148

149 150 151 152 153154

1.530

1

2 3

4

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Factor of Safety vs. Time

FactorofSafe

ty

Time

1.0

1.2

1.4

1.6

1.8

2.0

0 5 10 15 20

Note that the same

circle is used as

obtained from the

pseudostatic

analysis !


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Analysis repeated using shear strength = 80 percent of peak value for all soils to

account for some pore pressure generation during cycling.


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35

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1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

101 102 103 104 105 106

107108 109 110 111 112

113114115116117118

119120 121 122 123 124

125 126 127 128129 130

131 132 133 134 135136

137 138 139 140 141142143 144 145 146 147148

149 150 151 152 153154

1.365

1

2 3

4

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Factor of Safety vs. Time

Factoro

fSafety

Time

1.0

1.2

1.4

1.6

1.8

0 5 10 15 20


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Makdisi - Seed AnalysisWednesday, August 17, 2011

12:45 PM


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Makdisi - Seed Analysis (cont.)Wednesday, August 17, 2011

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More on the yield acceleration -

The yield acceleration, ay, is equal to the horizontal acceleration (g) applied to the potential failure

mass that produces a factor of safety of 1.0 (see example below). It can be determine from limit

equilibrium or other methods. The yield acceleration for the example below varies from 0.26 to 0.31

g depending on the undrained shear strength, Su, used for the embankment properties.

The yield coefficient, ky, is equal to the yield acceleration (g) divided by g; hence it is unitless. The

yield coefficient for the below example varies from 0.26 to 0.31 (unitless)


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Makdisi - Seed Analysis with Deformation Analysis p. 1 of 2Wednesday, August 17, 2011

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Makdisi - Seed Analysis with Deformation Analysis p. 2 of 2Wednesday, August 17, 2011

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Based on finite difference or finite element techniques

Full dynamics modeled

Deformation can be estimated using elasto-plastic or other constitutive

models

Required advanced training

Dealt with in more detail in CVEEN 7330

Slope geometry for analysis for FDM

Advanced Numerical MethodsWednesday, August 17, 2011

12:45 PM


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Acceleration time history (m/s^2 )applied at base of model

Acceleration time history (m/s^2 )

applied at crest of embankment

Horizontal displacement (m) predicted by model for weak shallow foundation

layer with phi = 20 deg. at end of 35 s of strong motion

Advanced Techniques (cont.)Wednesday, August 17, 2011

12:45 PM


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Horizontal displacement (m) predicted by model for liquefied shallow

foundation layer with phi = 10 deg. at end of 35 s of strong motion

Advanced Techniques (cont.)Wednesday, August 17, 2011

12:45 PM


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Summary of Embankment Stability AnalysesWednesday, August 17, 2011

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Summary of Embankment Stability Analyses (cont.)Wednesday, August 17, 2011

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Summary of Embankment Stability Analyses (cont.)Wednesday, August 17, 2011

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BlankWednesday, August 17, 2011

12:45 PM